Neither and Matching Signals

Separate NOR, NAND, XNOR and AND using a row that exposes the difference.

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Use Boolean 0 and 1 only. AND needs both ones; inclusive OR needs at least one. XOR of two bits is 1 when they differ. NOT reverses one bit. NOR = NOT (A OR B), NAND = NOT (A AND B), and XNOR = NOT (A XOR B). Check all four input pairs to compare complete rules. Use paper or screen, not real wiring or voltage measurements.

Worked example

At A = 1 and B = 0, OR is 1, so NOR is 0. AND is 0, so NAND is 1. The same input pair separates neither from not both.

Neither accepts only 00. Same accepts 00 or 11. An odd-count XOR chain accepts one or three one inputs. — Name the question before choosing the rule. These are logical values, not universal voltages.

Would you believe it?

Different triples can have the same odd-parity value: 001 and 010 each contain one 1. Two positions differ, yet both parity outputs are 1. Matching parity alone does not prove matching data.

Texas Instruments: three-input XOR function table

Question 1 At A = 0 and B = 1, what is NOR? 0 1 2

Question 2 Which input pair makes NAND equal 1 but NOR equal 0? 00 01 11

Question 3 At A = 0 and B = 0, what is XNOR? 0 2 1

Question 4 Which pair proves that AND and XNOR are not the same rule? 11 00 10

Question 5 Two rules agree at 11. Does this alone prove they agree for every Boolean pair? Yes; one matching row is enough. No; check 00, 01 and 10 too. Only if the output is 1.

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